Problem 1135 (difficulty: 3/10)

For which values of \(\displaystyle x\) do the following sequences converge? On which intervals do they converge uniformly?

\(\displaystyle \frac{x^n}{1+x^n} \quad \root{n}\of{1+x^{2n}} \quad \sqrt{x^2+\frac1n} \)

Give me another random problem!